The least common multiple of two integers is 36 and 6 is their greatest common divisor. What is the product of the two numbers?
Answer: Let $a$ and $b$ be the two integers. We can use the identity $\gcd(a,b) \cdot \mathop{\text{lcm}}[a,b] = ab$. Substituting gives that the answer is $36 \cdot 6 = \boxed{216}$.